Foliations with trivial canonical bundle on Fano 3-folds

TL;DR

This paper classifies foliations with trivial canonical bundle on Fano 3-folds with Picard rank one, and as a consequence, classifies holomorphic Poisson structures on these 3-folds.

Contribution

It provides the first classification of such foliations and Poisson structures on Fano 3-folds with Picard rank one, expanding understanding of their geometric structures.

Findings

Classified irreducible components of the space of foliations on these 3-folds.

Established a classification of holomorphic Poisson structures on the same class.

Connected the classification of foliations to Poisson geometry on Fano 3-folds.

Abstract

We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.